1. Field of the Invention
The present invention relates to testing apparatuses utilized in connection with a wind tunnel. The invention concerns, more particularly, a wind tunnel testing apparatus that is suitable for determining fluid forces on a variety of spherical or non-spherical objects, including a sport ball such as a soccer ball.
2. Description of Background Art
A soccer ball conventionally includes a paneled casing that surrounds an inflatable bladder. The casing is formed from a plurality of durable, wear-resistant panels that are stitched together along abutting edges to form a closed surface. The bladder, located on the interior of the casing, is formed of a material that is substantially impermeable to air and includes a valved opening, accessible through the casing, to facilitate inflation of the bladder. When inflated, the bladder expands and places a uniform outward pressure on the casing, thereby inducing the casing to take a substantially spherical shape. In addition, a lining may be positioned between the bladder and casing to provide protection for the bladder.
The panels that form the casing of the conventional soccer ball correspond with the various faces of a regular, truncated icosahedron. An icosahedron is a polyhedron having twenty faces. The term regular, when applied to an icosahedron, denotes a configuration wherein each of the twenty faces is an equally-dimensioned, equilateral triangle. A regular icosahedron, therefore, includes twenty equilateral triangular faces and twelve vertices that are formed where points of five triangular faces meet. A regular, truncated icosahedron is a regular icosahedron, as described, wherein each of the twelve vertices are removed, thereby converting the vertices into twelve pentagonal faces and converting each triangular face into a hexagonal face. Accordingly, a regular, truncated icosahedron is a polyhedron having thirty-two faces, twelve of which are equilateral pentagons and twenty of which are equilateral hexagons, and sixty vertices formed where the points of three faces meet.
The conventional soccer ball casing, which is modeled on the regular, truncated icosahedron, includes thirty-two panels composed of twenty equilateral hexagonal panels and twelve equilateral pentagonal panels. The panels are stitched together along abutting edges, the stitches being located on the interior portion of the casing. The internal pressure imparted by the bladder causes each panel of the traditional soccer ball to bow outward, thereby inducing a substantially spherical shape in the soccer ball.
During a soccer match or practice session, the soccer ball is generally manipulated by the feet of an individual in order to advance the soccer ball toward a goal. More specifically, the individual may kick the soccer ball. When kicked, the soccer ball may follow a trajectory that arcs upward, extends along a low, straight path, or curves left or right, for example. One factor that affects the trajectory of the soccer ball is the various physical characteristics of the soccer ball, which include, the depth of the seams between adjacent panels, the surface properties of the panels (e.g., rough, smooth, or dimpled), and the dimensions of the soccer ball, for example. In addition to the physical characteristics of the soccer ball, the spin and velocity imparted to the soccer ball by the individual also affect the trajectory.
As the soccer ball passes through the air, various fluid forces affect the trajectory, including a drag force and a side force. The drag force operates to slow the overall velocity of the soccer ball, thereby impeding forward motion of the soccer ball. The side force, which is orthogonal to the drag force and the spin axis of the soccer ball, causes the soccer ball to follow a curving trajectory or a downward trajectory. The degree of drag force and side force that operate upon the soccer ball to affect the trajectory depend upon the physical characteristics, spin, and velocity of the soccer ball, for example.
The total drag force upon a soccer ball includes two components: frictional drag and parasitic drag. Frictional drag occurs as a result of shear forces that act upon the soccer ball. As the soccer ball passes through the air, various molecules within the air contact the surface of the soccer ball and reduce the overall kinetic energy of the soccer ball through frictional losses. Parasitic drag forms the largest contributor of the total drag force and is a combination of all other forms of drag. For example, parasitic drag includes pressure drag, which reduces the kinetic energy of the soccer ball through differences in pressure between a front area and a rear area of the soccer ball. As the soccer ball moves through the air, a wake is formed behind the soccer ball (i.e., in the rear area of the soccer ball). In comparison with the pressure of the air that extends around the front area of the soccer ball, the pressure within the wake is significantly lower. In effect, therefore, a pressure difference is formed between the front and rear areas of the soccer ball. Given that the pressure in the rear area is less than the pressure in the front area, a rearwardly-directed force (i.e., pressure drag) impedes the motion of the soccer ball through the air.
The degree to which pressure drag affects the trajectory of the soccer ball depends, in part, upon the physical characteristics and velocity of the soccer ball. Research indicates that air moving over a perfectly smooth sphere separates (i.e., forms a wake) at a point positioned at approximately 80 degrees from the front area of the ball. Soccer balls, however, are not smooth spheres due to the seams and surface properties of the panels. In effect, the seams cause the air to become turbulent, thereby causing the air moving over the soccer ball to form a wake at a point that is positioned as much as 120 degrees from the front area of the ball. The initial velocity of the soccer ball also has an effect upon the drag force. In general, the drag force is proportional to the velocity of the soccer ball such that a greater velocity imparts greater drag forces. Accordingly, the physical characteristics and velocity of the soccer ball have an effect upon the trajectory of the soccer ball.
The side force also affects the trajectory of the soccer ball by causing the soccer ball to follow a curving trajectory or a downward trajectory, for example. The side force is orthogonal to both the drag force and the spin axis of the soccer ball. At relatively low angular velocities, the air follows the rotation of the soccer ball due to viscous, non-slip conditions at the surface of the soccer ball. When the soccer ball rotates at relatively high angular velocities, however, the air flow on one side of the soccer ball advances with the direction of the rotation, while the air flow on the other side of the soccer ball is impeded by the rotation. The air flowing with the rotation gains energy and exhibits a tendency to adhere to the surface of the soccer ball before separating to form the wake. The air flowing against the rotation, however, exhibits a greater tendency to separate from the surface and form a wake. This difference in separation points induces a pressure differential between the two sides of the soccer ball and results in the side force. As with pressure drag, the seams and surface properties of the panels may affect the degree of turbulence in the air, thereby affecting the side force acting upon the soccer ball.
As discussed above, the fluid forces acting upon the soccer ball depend upon the physical characteristics, spin, and velocity of the soccer ball, thereby affecting the overall trajectory of the soccer ball. The fluid forces include the drag force and the side force. Whereas the drag force operates to slow the overall velocity of the soccer ball, the side force causes the soccer ball to follow a curving trajectory or a downward trajectory.